In my example I used 18 gauge wire with a 3.5mm inner diameter jump ring. Since I am making my European 4-in-1 bracelets using sterling silver wire I will use the AWG measurements. I will need to find the AWG millimeter measurement for 18 gauge wire; 1.02mm. Now I can calculate the AR:
AR = 3.5 ÷ 1.02 = 3.43
Now I need to find a 20 gauge jump ring with that same AR. Since we know the desired AR is 3.43 and we know the AWG for 20 gauge wire is 0.81mm, we need to find out the jump ring's inside diameter.
3.43 = ID ÷ 0.81
To get the ID, multiply both sides of the = sign by 0.81 (remember algebra!). This will result in:
0.81 x 3.43 = ID
2.78mm = ID
You would need to purchase 20 gauge 2.75mm chainmaille jump rings. (Millimeter size jump rings do not come in 2.78mm, so I rounded to the closest size available).
Aspect ratios for chainmaille jump rings usually range between 2.9AR and 7.0AR. Each chainmaille weave will have a range of aspect ratios that will work. Below that range, the jump rings are too "thick" and the weave is either impossible to weave or so stiff that it is impractical. Above the range of appropriate ARs are rings that are probably weaveable, but the result will be a very loose weave.
Luckily for all of us, there are several sites online that have in-depth explanations and charts that do the math for us! Several chainmaille jump ring sellers recommend sizes for common chainmaille weaves. I will leave you with a quick reference:
If the wire gauge is the same: smaller inside diameter = smaller AR; larger ID = larger AR
If the inside diameter is the same: thicker wire = smaller AR; thinner wire = larger AR
The smaller the AR, the tighter the weave
The larger AR, the looser the weave